Leaky and surface wave diffraction by an asymmetric impedance half plane

Abstract

An exact solution is obtained for the problem of a leaky or surface wave incident on an impedance half plane in a homogeneous, isotropic medium. The impedance half plane is asymmetric, i.e., with different constant surface impedances at the upper and lower faces, respectively. The incident leaky wave propagates in a direction normal to the edge of the half plane.The diffraction problem leads to a set of two coupled Wiener–Hopf equations, from which two Hilbert problems on a new contour are obtained and solved. The Wiener–Hopf–Hilbert method is used. Expressions for the geometrical optical field are also derived and results arc discussed from the point of view of the uniqueness of the solution.